# nLab Sandbox

$\begin{array}{cc} \text{positions of horizontal steps} & \text{positions of vertical steps} \\ \mu_1 \lt \mu_2 \lt \cdots \lt \mu_p & \nu_1 \lt \nu_2 \lt \cdots \lt \nu_p \end{array}$

### Context

#### Analytic geometry

analytic geometry (complex, rigid, global)

## Basic concepts

analytic function

analytification

## Theorems

GAGA

###### Definition

(ScholzeWeinstein20, Definition 6.2.1)

Let $R$ be a perfectoid ring. The tilt of $R$ is

$R^{\flat}=\underset {\underset{x\mapsto x^{p}}{\leftarrow}} {\lim}R$

A priori this is a topological multiplicative monoid, so turn it into a topological ring we equip it with the addition structure given by

$(x+y)^{(i)}=\lim_{n\to\infty}(x^{(i+n)}+y^{(i+n)})^{p^{n}}.$

Last revised on December 3, 2022 at 18:02:15. See the history of this page for a list of all contributions to it.